111

Prompt

(function() { 'use strict'; function expandPPS(seq, nCount, maxLength) { if (!Array.isArray(seq)) return []; if (seq.length === 0) return []; var Y = seq.length; var X = seq[Y - 1]; var hasMax = (maxLength !== null && maxLength !== undefined); if (X === 0) { var zeroRes = seq.slice(0, -1); return hasMax ? zeroRes.slice(0, maxLength) : zeroRes; } if (X > Y) { throw new Error('末项值 ' + X + ' 作为列标超出序列长度 ' + Y + '，无法找到坏根。'); } var B = seq[X - 1]; var L = Y - X; var v; var equalCount = 0; for (var col = X + 1; col <= Y - 1; col++) { if (seq[col - 1] === B) equalCount++; } if (equalCount >= 2) { v = B; } else { var strongStart = B + 1; var strongEnd = X - 1; var foundCol = null; if (strongStart <= strongEnd) { for (var col2 = strongEnd; col2 >= strongStart; col2--) { if (seq[col2 - 1] <= B) { foundCol = col2; break; } } } v = (foundCol !== null) ? foundCol : B; } var totalLen = Y + nCount * L - 1; var res = new Array(totalLen); for (var i = 0; i < X; i++) { res[i] = seq[i]; } for (var i = X; i < Y - 1; i++) { res[i] = seq[i]; } res[Y - 1] = v; for (var i = X; i < Y; i++) { var baseVal = (i === Y - 1) ? v : seq[i]; var ge = baseVal >= X; var maxK = (i === Y - 1) ? (nCount - 1) : nCount; for (var k = 1; k <= maxK; k++) { var pos = i + k * L; if (pos >= totalLen) continue; if (ge) { res[pos] = baseVal + k * L; } else { res[pos] = baseVal; } } } return hasMax ? res.slice(0, maxLength) : res; } function executeDnOperation(seq, n) { var targetLen = seq.length + (n - 1); return expandPPS(seq, 1000, targetLen); } function executeTnOperation(seq, n) { var res = seq.slice(); for (var i = 0; i < n; i++) { if (res.length === 0) break; res = res.slice(0, -1); } return res; } function parse(str) { if (!str || !str.trim()) return []; var parts = str.split(','); var seq = []; for (var i = 0; i < parts.length; i++) { var token = parts[i].trim(); token = token.replace(/<sub>[\s\S]*?<\/sub>/gi, ''); token = token.replace(/[_{}\s]/g, ''); if (/^w$/i.test(token)) { seq.push(Infinity); } else { var v = parseInt(token, 10); if (isNaN(v)) return null; seq.push(v); } } return seq; } function ensureArray(expr) { if (Array.isArray(expr)) return expr; if (expr && typeof expr === 'object') { var arr = []; for (var key in expr) { if (expr.hasOwnProperty(key) && !isNaN(parseInt(key))) { arr.push(expr[key]); } } return arr; } return null; } function displayPlain(expr) { if (expr === undefined || expr === null) return '0,2'; if (typeof expr === 'number') return String(expr); var arr = ensureArray(expr); if (arr === null) return '0,2'; if (arr.length === 0) return '(empty)'; return arr.join(','); } function displayHtml(expr) { if (expr === undefined || expr === null) return '0,2'; if (typeof expr === 'number') return String(expr); var arr = ensureArray(expr); if (arr === null) return '0,2'; if (arr.length === 0) return '(empty)'; var parts = arr.map(function(val, idx) { return val + '_{' + (idx + 1) + '}'; }); return parts.join(','); } function displayLatex(expr) { if (expr === undefined || expr === null) return '0,2'; if (typeof expr === 'number') return String(expr); var arr = ensureArray(expr); if (arr === null) return '0,2'; if (arr.length === 0) return '\\emptyset'; return arr.join(','); } function isLimit(expr) { if (typeof expr === 'number') return expr > 0; var arr = ensureArray(expr); if (!arr) return false; return arr.length > 0 && arr[arr.length - 1] > 0; } function compare(a, b) { if (typeof a === 'number') a = [a]; if (typeof b === 'number') b = [b]; var arrA = ensureArray(a); var arrB = ensureArray(b); if (!arrA || !arrB) { if (!arrA && !arrB) return 0; return arrA ? 1 : -1; } var len = Math.min(arrA.length, arrB.length); for (var i = 0; i < len; i++) { if (arrA[i] < arrB[i]) return -1; if (arrA[i] > arrB[i]) return 1; } if (arrA.length < arrB.length) return -1; if (arrA.length > arrB.length) return 1; return 0; } function FS(expr, n) { if (typeof expr === 'number') { expr = [expr]; } var arr = ensureArray(expr); if (!arr || arr.length === 0) return []; var nNum = Number(n); if (nNum === 0) { return arr.slice(0, -1); } if (arr.length === 2 && arr[0] === 0 && arr[1] === 2) { var result = []; for (var i = 0; i <= nNum; i++) { result.push(i); } return result; } return expandPPS(arr, nNum); } function init() { return [[0, 2]]; } if (typeof register_notation === 'function') { register_notation({ id: '2-pps4', name: '2-pps4', display: { plain: displayPlain, html: displayHtml, latex: displayLatex, from_display: parse }, from_display: parse, is_limit: isLimit, compare: compare, FS: FS, init: init, dn: executeDnOperation, tn: executeTnOperation }); } else { console.error('[pps4s2] register_notation is not available.'); } })(); 分析这个记号(2-pps4)和康托范式的对应 从0,2展开能得到就是标准的，标准的符合字典序，你只要考虑标准的。 你的分析只要给出2-pps4表达式=康托范式，以及需要用到的证明(不需要解释，只要你能看懂的证明就行，但是必须要保证你能看懂)(txt格式，方便复制)，不要有其他内容，最多说明是猜测还是确定的。 要求，仅此次对话，禁止调用工具